Dixon Shuttleworth has a large sum of money that we wants to invest to finance his retirement. He has been presented with three options. The first investment offers a 5% return for the first 5 years, a 10% return for the next 5 years, and a 20% return thereafter. The second investment offers 10% for the first 10 years and 15% thereafter. The third investment offers a constant 12% rate of return. Determine which of these investments is the best for Dixon if he plans to retire in the following number of years:

a. 15 years

b. 20 years

c. 30 years